Modeling evaluation of a direct-expansion solar-assisted heat pump water heater using R410A

Accepted Manuscript Title: Modeling evaluation of a direct-expansion solar-assisted heat pump water heater using R410A Author: X.Q. Kong, Y. Li, L. Lin, Y.G. Yang PII: DOI: Reference:

S0140-7007(17)30040-3 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.020 JIJR 3532

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

24-8-2016 16-1-2017 20-1-2017

Please cite this article as: X.Q. Kong, Y. Li, L. Lin, Y.G. Yang, Modeling evaluation of a directexpansion solar-assisted heat pump water heater using R410A, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.020. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Modeling evaluation of a direct-expansion solar-assisted heat pump water heater using R410A X.Q. Kong1, Y. Li, L. LIN, Y.G. Yang School of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao 266590, China

Highlights:  A direct-expansion solar-assisted heat pump system by using R410A as refrigerant is designed.  A numerical model is developed to estimate the thermal performance of the system.  The effects of the refrigerant charge quantity on the performance parameters of the system are analyzed.  The effects of various parameters have been simulated and analyzed on the thermal performance of the system.

Abstract:

A direct-expansion solar-assisted heat pump (DX-SAHP) system by using R410A as refrigerant is described, which can supply domestic hot

water during the whole year. Based on the distributed parameter and homogeneous flow models of collector/evaporator and condenser, the

lumped parameter models of compressor and electronic expansion valve, and the refrigerant charge model, a numerical model is developed to

estimate the thermal performance of the system. Given the structure parameters, meteorological parameters, initial and final water temperature,

for a fixed superheat degree, the effects of the refrigerant charge quantity on the performance parameters of the system are analyzed, such as

compressor power, heat gain of collector, heating time, collector efficiency and system COP. Furthermore, for a fixed refrigerant charge quantity,

the effects of various parameters, including solar radiation, ambient temperature, compressor speed and initial water temperature, have been

simulated and analyzed on the thermal performance of the system.

Keywords: Solar-assisted heat pump; Direct-expansion; R410A; Performance; Modeling

Nomenclature A

area (m2)

C

specific heat (J kg-1 K-1)

d

diameter of the pipe (m)

1

Corresponding author. Tel.: +86-532-8605-7912; Fax: +86-532-8605-7987. E-mail address: [email protected]. (X.Q. Kong).

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F

efficiency of the ribs (dimensionless)

F′

collector efficiency factor (dimensionless)

h

specific enthalpy (J kg-1)

I

solar radiation intensity (W m-2)

L, l

length (m)

m

mass flow rate (kg s-1)

M

mass (kg)

N

compressor rotational speed (r min-1)

p

pressure (Pa)

Q, q

heat gain (W)

q∞

sky radiation (W m-2)

S

difference between the solar radiation absorbed and the total radiation heat loss (W m-2)

s

slip ratio (dimensionless)

T

absolute temperature (K)

t

Celsius temperature (°C)

U

overall heat-transfer coefficient (W m-2 K-1)

Ub

dimensionless number (dimensionless)

UL

overall heat loss coefficient (W m-2 K-1)

v

specific volume (m3 kg-1)

V

volume (m3)

Vd

displacement volume rate (m3 rev-1)

W

power (W)

w

distance of the pipe (m)

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Greek symbols α

convective heat transfer coefficient (W m-2 K-1)

τ

time (s)

γ

void fraction (dimensionless)

ρ

density (kg m-3)

ξ

Stefan-Boltzmann constant (W m-2 K-4)

λ

thermal conductivity coefficient (W m-1 K-1)

ε

emissivity (dimensionless)

δ

thickness (m)

η

efficiency (dimensionless)

κ

polytropic index (dimensionless)

φ

volumetric efficiency of compressor (dimensionless)

ζ

heat leakage coefficient of water tank (dimensionless)

θ

absorptivity (dimensionless)

Subscripts a con

ambient air condenser

col

collector/evaporator

com

compressor

dis

discharge

e

electronic expansion valve

f

final

g

gas

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i

inlet, inside

ini

initial

j

jth infinitesimal section

k

kth infinitesimal time step

l

liquid

n

total number of infinitesimal section

o

outlet, outside

p

collector plate

pip

pipe

r

refrigerant

sp

single-phase state

suc

suction

tp

two-phase state

v

vapor

w

water

z

total number of time steps

1. Introduction During the last years, there has been a continuing interest in the combination of the heat pump and solar thermal system. Solar energy can be used to heat the refrigerant in the evaporator of a heat pump, by employing a solar collector as the evaporator, which is called a direct-expansion solar-assisted heat pump (DX-SAHP) system. Compared to the air-source heat pump system alone, the DX-SAHP system operates at higher evaporating temperature due to effective absorption of solar thermal energy which therefore results in a higher heat pump performance, and the refrigerant in the collector

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undergoes a phase change at a relating low temperature which yields high collector efficiency than that of a straight solar thermal system [1]. In virtue of superior thermodynamic performance, many theoretical and experimental studies have focused on DX-SAHP systems by researches worldwide, including system structure, thermal performance, working fluid characteristics, operational control, numerical simulation, economic analysis, etc [1-12]. Torres Reyes et al. presented a theoretical and experimental exergy analysis of a DX-SAHP system for air heating. An experimental prototype was tested to determine exergetic efficiency, total system irreversibility and component irreversibilities [2]. Huang et al. investigated an integral type solar-assisted heat pump water heater. A long-term reliability test was carried out and a performance model was derived which agreed very well with experimental data. Based on that, a simple linear correlation for the performance evaluation of the system was derived [3-5]. Kuang et al. investigated the long-term performance of a DX-SAHP system for domestic use, which could offer space heating, air conditioning and hot water. A review on this work has indicated that the system could maintain a long-term good operation with low running cost under various working conditions [1]. Li et al. built a DX-SAHP water heater experimental set-up with rotary-type hermetic compressor of rated input power 750W. Through experimental research and exergy analysis, some methods were suggested to improve the whole system’s thermal performance, including the design optimization of each component [6,7]. Kara et al. presented a mathematical model of a DX-SAHP system with a 4m2 bare flat-plate collector as the evaporator for heating an office. The exergy efficiency values for the individual components of the system ranged from 10.74% to 88.87% [8]. Chaturvedi et al. investigated the use of two-stage DX-SAHP systems for high temperature applications in the range of 60–90 °C. The thermal performance of the system was analyzed, and a method for sizing the solar collector area and the heat pump compressor displacement capacity was proposed [9]. Chow et al. introduced a numerical model of the DX-SAHP system for water heating. With the use of the Typical Meteorological Year weather data of Hong Kong, the system was found achieving a year-average coefficient of performance (COP) of 6.46, which was much better than the conventional heat pump system performance [10]. Moreno-Rodríguez et al. studied a DX-SAHP system which mainly consisted of a compressor with a rated capacity of 1.1 kW and collectors with a total area of 5.6 m2. The analysis was conducted over the

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course of a year. The experimental COP was between 1.7 and 2.9 when the domestic hot water tank temperature was 51 °C [11]. Fernández-Seara et al. studied experimentally the performance of a DX-SAHP water heating system under zero solar radiation conditions by placing the solar collectors into a climate chamber. Performance parameters to evaluate the energy efficiency were obtained, and a characteristic COP of the system was 3.23 under zero solar radiation condition [12]. From the present literatures about DX-SAHP systems, it could be observed that R22 was a popular choice as refrigerant in the DX-SAHP systems due to good thermo physical and thermodynamic properties. However, R22 has an ozone depletion potential (ODP) of 0.05, which has been targeted by the Montreal protocol 1987 to be phased out in new equipment. Additionally, many countries are enforcing a ban of HCFC-based refrigerants for new installations. A number of R22 alternatives have been researched in recent years. Among the alternatives, R410A has been increasingly available in air-conditioning and heat pump applications [13, 14]. R410A is a blend of HFCs, which has a zero ODP but a slightly higher global warming potential (GWP) than R22. Zhang et al. investigated experimentally condensation heat transfer and pressure drop of R22, R410A and R407C. The results showed that as a substitute for R22, R410A had more advantages in view of the characteristics of condensation heat transfer and pressure drop than R407C [15]. The condensation pressure drop characteristics for R22, R134a and R410A were also studied by Son et al. The experimental results showed that the condensation pressure drop of R134a was higher than that of R22 and R410A for the same mass flux [16]. Kaew-On et al. studied the evaporation heat transfer coefficients and pressure drops of R410A and R134a. The experimental data showed that the evaporator heat transfer coefficients of R410A were about 20-50% higher than those of R134a, while the pressure drops of R410A were about 50-100% lower than those of R134a [17]. Huang et al. investigated the performance of the indoor coil in a split-type air-source heat pump with R22 and R410A. The results showed that the capacity of the evaporator with R410A was greater than that with R22 [18]. As one of the leading replacements for R22, R410A has been used as a working fluid in many cooling and heating applications [19-28]. However, there have been very few reports about a DX-SAHP system by using R410A as refrigerant. In this paper, a DX-SAHP system is presented for hot water supply during the whole year, and the working fluid is chosen

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to be R410A. A numerical model of the system is introduced, including the distributed parameter models of solar collector/evaporator and condenser, the lumped parameter models of compressor and electronic expansion valve and the refrigerant charge model. The thermal performance of the system is analyzed, including the effects of various parameters on system performance. 2. System description The DX-SAHP system by using R410A as refrigerant, designed to produce domestic hot water, is illustrated schematically in Fig. 1. It mainly consists of a solar collector/evaporator, a rotary-type and hermetic compressor, a hot water tank with an immersed condensing coil and an electronic expansion valve. The refrigerant R410A enters the pipes of the solar collector/evaporator, where it can absorb heat from the solar energy and/or ambient air and is then vaporized. Vapor from the solar collector/evaporator passes into the compressor, and hence comes into the condenser where it is cooled by the water in the hot water tank. The condensed liquid refrigerant leaving the condenser passes through the electronic expansion valve and forms liquid/vapor mixture, and then enters the solar collector/evaporator. The specification of the main components used in this study is listed in Table 1. 3. Development of the model Based on the distributed parameter and homogeneous flow models of the solar collector/evaporator and the condenser, the lumped parameter models of the compressor and the electronic expansion valve, and the refrigerant charge model, a numerical model is developed to estimate the thermal performance of the DX-SAHP system. The following assumptions are made for the numerical analysis of the thermal characteristics: (1) The DX-SAHP system is at steady-state within the time interval. (2) Pressure drop is negligible in collector/evaporator, condenser and pipes. (3) Compression of the refrigerant vapor is assumed to follow a polytropic process. (4) Expansion of refrigerant liquid is considered to be isenthalpic. (5) Temperature stratification in hot water tank is ignored.

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In addition, a fast calculation model for the thermodynamic and transport properties of the chosen refrigerant R410A is presented, which is based on the polynomial function fitting method and the Martin-Hou equation of state [29,30]. The source data is calculated from REFPROP7 [31]. This method can guarantee the calculation stability and high calculation speed, and it is also convenient in case of simulation of the DX-SAHP system for its uniform expression. 3.1. Solar collector/evaporator The DX-SAHP system uses a series of bare flat-plate solar collector without any glazing or back insulation as well as the evaporator for the refrigerant R410A. It consists of four aluminum absorber plates in parallel with the total area of 4.2 m2. In general, the refrigerant in the collector/evaporator passes through two-phase region and superheat region in turn. Along the flow direction, the collector pipe can be divided into many infinitesimal sections with equal enthalpy difference, as shown in Fig. 2. Tr,i and Tr,o are the temperatures of the refrigerant at the inlet and outlet, hr,i and hr,o are the inlet and outlet enthalpy of the refrigerant, and l is the pipe length of the infinitesimal section. In the mathematical model of the solar collector/evaporator, it is assumed that the refrigerant flow in the pipe is a one-dimensional homogeneous flow along with axis, and that the mass diffusion and heat conduction of the refrigerant is neglected along with axis. The heat gain of the refrigerant in the solar collector/evaporator is as follows: Q r  m r ( hr,o  hr,i )

(1)

where Qr is the heat gain of the refrigerant in the solar collector/evaporator, mr is the refrigerant mass flow rate, and Trm is the average temperature of the refrigerant at the inlet and outlet of the infinitesimal section of the solar collector/evaporator. The useful heat gain of solar collector/evaporator can be evaluated as follows [32-35]: Q col  Acol F [ S  U L (T rm  T a )] '

(2)

where Qcol is the useful heat gain of solar collector/evaporator, Acol is the area of the infinitesimal section of the solar collector/evaporator, F' is the collector efficiency factor, S is the difference between the solar radiation absorbed by the collector per unit area and the total radiation heat loss from the collector surface, UL is the overall heat loss coefficient of the collector plate, and Ta is the ambient air temperature.

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Acol is given by: Acol 

l

(3)

A

L

where A is the total area of the solar collector/evaporator, and L is the total length of the pipe. Assuming that the thermal resistance of the bond between the tube and the collector plate can be neglected, F' is given by [33]:

F   F  1  F   d / w 

(4)

where F is the fin efficiency, d is the external diameter of the pipe, and w is the distance between the pipes. F can be evaluated using the following correlation： F 

tan h U b

(5)

Ub

where Ub is the dimensionless number, which is given by： Ub 

wd

UL

2

 p p

(6)

where λp is the thermal conductivity of the collector plate, and δp is the thickness of the collector plate. The symbol S is calculated by: S   I   q0

(7)

where θ is the absorptivity of the collector plate, I is the solar radiation intensity on the collector plate, ε is the emissivity of the collector plate, and q0 is the difference between the emissive power per unit area from a black body at the ambient air temperature and the emissive power from the sky, as given: q 0   Ta  q  4

(8)

where ξ is the Stefan-Boltzmann constant with the value of 5.67×10-8 W m-2 K-4, and q∞ is the sky radiation. The symbol UL can be expressed by: U L    4  T a

3

(9)

where α is the convective heat transfer coefficient. Assuming no heat loss, heat balance equation of solar collector/evaporator is shown as follows: 9

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Q r  Q col

(10)

3.2. Compressor The lumped parameter method is used to establish the mathematical model of the compressor. For a small-scaled rotary-type and hermetic compressor, the refrigerant mass flow rate is given by: mr 

N Vd

(11)

60 suc

where N is the compressor rotational speed, vsuc is the specific volume of the refrigerant at the inlet of the compressor, φ is the volumetric efficiency of the compressor, and Vd is the displacement volume rate of the compressor. The pressure drop at the inlet and outlet of the compressor is neglected, and the electrical power consumption of the compressor can be determined by the following equation [36]:

W com  m r

p suc  suc

 com

   p dis  - 1   p suc 



 1

   



  1  

(12)

where psuc and pdis are the suction pressure and discharge pressure of the compressor, ηcom is the total efficiency of the compressor, and κ is the polytropic index of the refrigerant vapor. The discharge temperature of the compressor is given by:  1

T dis

 p  T suc  dis  p suc

   



(13)

where Tsuc and Tdis are the suction temperature and discharge temperature of the compressor, respectively. 3.3. Condenser The condenser is composed of a serpentine copper tube, which is immersed in the hot water tank. Using the same method as that of the solar collector/evaporator, along the flow direction of the refrigerant, the copper tube in the condenser can also be divided into many infinitesimal sections with equal enthalpy difference. The heat gain in the condenser can be calculated as follows: QW  M wCw

dT w d

(14)

where Qw is the heat gain in the condenser, Mw is the total mass of the water in water tank, Cw is the specific heat of water, Tw is the water temperature, and τ is the heating time. Considering heat loss of hot water tank, the condenser heat balance is shown as follows: Q w   Q r, con

(15) 10

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where Qr,con is the heat release of refrigerant in the condenser, and ζ is the heat leakage coefficient of water tank. Qr,con is expressed by: Q r , con  U con, o A con, o T rm ,con  T w 

(16)

where Ucon,o is the overall heat-transfer coefficient based on the outside area of the condenser tube, Acon,o is the outside area of the condenser tube, and Trm,con is the average temperature of the refrigerant at the inlet and outlet of the infinitesimal section of the condenser. Ucon can be calculated with: U con 

1 Acon ,o

 i Acon ,i



 con Acon ,o  con Acon , m



(17)

1

w

where  i is the convective heat transfer coefficient between refrigerant and inside wall surface of the condenser tube[37],

 w is the convective heat transfer coefficient between water and outside wall surface of the condenser tube, Acon,i is the inside area of the condenser tube, Acon,m is the average surface area of the condenser tube,  con is the thickness of the condenser tube, and  con is the thermal conductivity coefficient of the condenser tube. 3.4. Electronic expansion valve The throttling process in the electronic expansion valve is considered approximately to be isenthalpic, which is one of the important iterative criterions for the model convergence of the DX-SAHPWH system. The following expression is used: h e,i  h e,o

(18)

where he,i, he,o are the specific refrigerant enthalpy at the inlet and outlet of the electronic expansion valve, respectively. 3.5. Refrigerant charge quantity The refrigerant charge quantity is also an important criterion for the model convergence of the system. System refrigerant charge quantity is the sum of that in each component with single-phase or two-phase state. The two-phase refrigerant mainly exists in solar collector/evaporator, condenser, and connecting pipes. The two-phase refrigerant charge quantity Mtp can be calculated as following: M tp 



V 0

  v   1     l d V 

n

   j 1

j

 v, j  1   j   l, j V j 

(19)

where γ is the void fraction[38], ρl and ρv are the densities of saturated liquid and vapor of the refrigerant, V is the volume of

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the refrigerant, j is the jth infinitesimal section, and n is the amount of infinitesimal sections. The single-phase refrigerant can be divided into two types, including the superheated state and sub-cooled state. The single-phase refrigerant mainly exists in the superheated area in the collector/evaporator, the sub-cooled area in the condenser, superheated area in the condenser, the compressor and connection pipes. The single-phase refrigerant charge quantity Msp can be calculated as following: M sp 



V 0

n

 sp d V 



Vj

sp, j

(20)

j 1

where ρsp is the density of the single-phase refrigerant. The whole refrigerant charge quantity Mr of the system can be evaluated as follows: M r  M com  M

tp , col

M

M

tp , con

tp , pip

 M sp , col  M sp , con  M sp , pip

(21)

where Mcom is the compressor refrigerant charge quantity. Mtp,col, Mtp,con and Mtp,pip are the two-phase state refrigerant charge quantity in solar collector/evaporator, condenser coils and connecting pipes, respectively. Msp,col, Msp,con and Msp,pip are the single-phase state refrigerant charge quantity in solar collector/evaporator, condenser coils and connecting pipes, respectively. 3.6. Thermal performance evaluation The instantaneous collector efficiency ηk is the weighted average of that of all infinitesimal sections of the solar collector/evaporator pipe during the kth time step, which is defined as follows: 

n

k     

j 1

Q col , jl j   Acol , j I 

L

(22)

where the subscript k denotes the kth time step. The average collector efficiency η is the arithmetic mean of ηk during the whole heating process, which is defined by the following equation: 

z



    k  z  k 1



(23)

where z is the total number of time step. 12

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The instantaneous COP is defined as: COP

k

 Q w , k W com , k

(24)

where COPk is the instantaneous COP of the kth time step, and Wcom,k is the instantaneous compressor power at the kth time step. The average COP is shown as follows:  z  COP    Q w , k   k 1 

 z    W c o mk ,  k 1 

(25)

where COP is the average COP during the whole heating process. 3.7. System model solution Based on the mathematical model of the DX-SAHP system and the refrigerant thermodynamic cycle, the system thermal performance simulation program is established. The solution algorithm of the simulation program is shown in Fig.3, where Mr,cal and Mr,set are the calculated and set values of refrigerant charge quantity of the system. tw,cal and tw,set are the calculated and set values of the final water temperature in the hot water tank. 4. Discussion of results The various input parameters used in the simulation program of the DX-SAHP water heater are listed in Table 2. In the simulation process, only the analyzed parameter is changed, and the other parameters are still the initial values without change. What’s more, in the process of simulation, the superheat degree at the outlet of the collector/evaporator is kept 5 oC. 4.1. Effects of refrigerant charge quantity on the performance of the DX-SAHP system Effect of refrigerant charge quantity Mr on the compressor power Wcom is shown in Fig. 4. It is clearly seen that Wcom increases with the increase of water temperature tw when Mr keeps unchanged. In addition, for the same tw, Wcom also increases with the increase of Mr. This is because when Mr or tw increases, the pressure ratio of the compressor increases, which hence causes higher Wcom. When Mr is 1.68 kg, in the process of tw from 20.5 °C up to 50 °C, Wcom increases from 0.55 kW to 1.14 kW. On the other hand, when tw is equal to 50 °C, with the increase of Mr from 1.48 kg to 2.28 kg, Wcom increases from 1 kW to 1.22 kW. Therefore, in order to improve system thermal performance, the final temperature of hot 13

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water should not be set too high. Effect of Mr on heating time τ and useful energy gain of the collector Qcol are shown in Fig. 5 and Fig. 6, respectively. As Mr increases from 1.48 kg to 2.28 kg, a corresponding increase in the refrigerant mass flow rate is also evident. This causes the increment of Qcol and the decrement of τ. In the process of tw from 20.5 °C up to 50 °C, when Mr keeps 1.68 kg, τ is 68 min, and Qcol decreases from 4.08 kW to 3.14 kW. When Mr is up to 2.08 kg, τ is 63 min, and Qcol decreases from 4.27 kW to 3.6 kW. Effect of Mr on instantaneous collector efficiency ηk is shown in Fig. 7. It is clearly seen that ηk increases with the increase of M for the same tw. In addition, when Mr keeps unchanged, ηk decreases with the increase of tw. This is a result of the combined action of various factors, mainly including the refrigerant mass flow rate, evaporation temperature and superheat degree. In the process of tw from 20.5 °C up to 50 °C, when M keeps 1.68 kg, ηk decreases from 1.2 to 0.95. When Mr is up to 2.08 kg, ηk decreases from 1.3 to 1.1. It is also found that ηk can exceed 1.0, which is because when the temperature of the collector plate is lower than ambient air temperature, the collector could obtain useful energy gain from the surroundings. Effect of Mr on instantaneous coefficient of performance COPk is shown in Fig. 8. It can be concluded that COPk of different M presents an approximately linear relation with respect to tw, and there is little difference among different Mr. In other words, when Mr keeps unchanged, COPk decreases rapidly with the increase of tw, but for the same tw, Mr has little effect on COPk. When Mr is 1.68 kg, in the process of tw from 20.5 °C up to 50 °C, COPk decreases from 8.6 to 3.62. The reason is that with the increase of tw, the compressor power Wcom increases, but the heat gain at the condenser Qw decreases. 4.2. Effects of meteorological parameters on the performance of the DX-SAHP system Effect of solar radiation intensity I on system performance is shown in Fig. 9. It is clearly seen that with the increase of I, the average collector efficiency η and heating time τ decrease, but average coefficient of performance COP increases. In the process of I from 300 W m-2 up to 900 W m-2, η decreases from 2.1 to 1, COP increases from 4.1 to 6, and τ decreases from 85 min to 64 min. Results show that the increase of the solar radiation intensity has great effect to improve the performance

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of system. Effect of ambient temperature ta on system performance is shown in Fig. 10. As is shown, with the increase of ta from 0 °C up to 35 °C, heating time τ decreases from 88 min to 63 min, the average collector efficiency η increases from 0.8 to 1.24, and COP increases from 3.9 to 6.1. It is worth noting that when the surface temperature of the collector plate is lower than ambient temperature, the collector/evaporator could obtain useful energy gain from the surroundings, which results in an increase in collector efficiency, even bigger than 1.0. Therefore, it is concluded that the higher ambient temperature causes better system performance. 4.3. Effects of operational parameters on the performance of the DX-SAHP system Fig.11 shows the effect of compressor rotational speed N on system performance. With the increase of N, η has a gentle increase trend, while the COP and τ decreases rapidly. When N increases from 1500 r min-1 to 3300 r min-1, η increases from 0.76 to 1.19, COP decreases from 11.84 to 4.84, and τ decreases from 108 min to 62 min. With the increase of N, both the compressor power and the heating power increase, but the increase of heating power is lower than the increase of compressor power, which leads to the COP decreases. Effect of initial water temperature tw,ini on system performance is shown in Fig. 12. With the increase of tw,ini, η has a slight decrease, COP decreases gradually, and τ also decreases rapidly. When tw,ini increases from 5 °C to 30 °C, η decreases from 1.17 to 1.08, COP decreases from 6.55 to 4.75, and τ decreases from 102 min to 47 min. The results indicate that the increase of tw,ini can considerably reduce the heating time, which results in a decrease in the total energy consumption of the compressor. 5. Conclusions Based on the distributed parameter and homogeneous flow models of solar collector/evaporator and condenser, the lumped parameter models of compressor and electronic expansion valve, and the refrigerant charge model, a simulation program of a DX-SAHP water heater system using R410A is coded. For a fixed superheat degree at the outlet of the collector/evaporator, the effects of various parameters, including refrigerant charge quantity, solar radiation intensity,

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ambient temperature, compressor rotational speed, and initial water temperature, on the thermal performance of the system. The following conclusions are drawn from the present study. (1) As the refrigerant charge quantity increases, the useful energy gain of the collector and the compressor power increase, the heating time decreases, the instantaneous collector efficiency increases significantly, but it has little effect on the instantaneous coefficient of performance. (2) The thermal performance of the system is affected significantly by the variation of meteorological parameters. The heating time at the solar radiation intensity of 300 W m-2 is 32.8% higher than that of 900 W m-2, while the average COP is increased by about 46.3%. With the increase of ambient temperature from 0 °C up to 35 °C, the heating time is 28.4% lower and the average COP is 56.4% higher. (3) Operational parameters have also significant effects on the thermal performance of the system. The average COP at the compressor rotational speed of 1500 r min-1 is 144.6% higher than that of 3300 r min-1, while the heating time is decreased by about 42.6%. When the initial water temperature increases from 5 °C up to 30 °C, the heating time is decreased by about 53.9%. Acknowledgements This work was supported by the Shandong Province Higher Educational Science and Technology Program under the contract No. J11LD63, and the Huangdao District Science and Technology Program under the contract No. 2014-1-40. References [1] Y.H. Kuang, R.Z. Wang. Performance of a multi-functional direct-expansion solar assisted heat pump system. Solar Energy, 2006, 80(7): 795-803. [2] E. Torres Reyes, M. Picon Nuñez, J. Cervantes de G. Exergy analysis and optimization of a solar-assisted heat pump. Energy, 1998, 23(4): 337-344. [3] B.J. Huang, C.P. Lee. Performance evaluation method of solar-assisted heat pump water heater. Applied Thermal Engineering, 2007, 27(2-3): 568-575. [4] B.J. Huang, C.P. Lee. Long-term performance of solar-assisted heat pump water heater. Renewable Energy, 2004, 29(4): 633-639. [5] B.J. Huang, J.P. Chyng. Performance characteristics of integral type solar-assisted heat pump. Solar Energy, 2001, 71(6): 403-414. [6] Y.W. Li, R.Z. Wang, J.Y. Wu, Y.X. Xu. Experimental performance analysis on a direct-expansion solar-assisted heat pump water heater. Applied Thermal Engineering, 2007, 27(17-18): 2858-2868. 16

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[7] Y.W. Li, R.Z. Wang, J.Y. Wu, Y.X. Xu. Experimental performance analysis and optimization of a direct expansion solar-assisted heat pump water heater. Energy, 2007, 32(8): 1361-1374. [8] O. Kara, K. Ulgen, A. Hepbasli. Exergetic assessment of direct-expansion solar-assisted heat pump systems: Review and modeling. Renewable and Sustainable Energy Reviews, 2008, 12(5): 1383-1401. [9] S.K. Chaturvedi, T.M. Abdel-Salam, S.S. Sreedharan, F.B. Gorozabel. Two-stage direct expansion solar-assisted heat pump for high temperature applications. Applied Thermal Engineering, 2009, 29(10): 2093-2099. [10] T.T. Chow, G. Pei, K.F. Fong, Z. Lin, A.L.S Chan, M. He. Modeling and application of direct-expansion solar-assisted heat pump for water heating in subtropical Hong Kong. Applied Energy, 2010, 87(2): 643-649. [11] A. Moreno-Rodríguez, A. González-Gil, M. Izquierdo, N. Garcia-Hernando. Theoretical model and experimental validation of a direct-expansion solar assisted heat pump for domestic hot water applications. Energy, 2012, 45(1): 704-715. [12] J. Fernández-Seara, C. Piñeiro, J. Alberto Dopazo, F. Fernandes, P.X.B. Sousa. Experimental analysis of a direct expansion solar assisted heat pump with integral storage tank for domestic water heating under zero solar radiation conditions. Energy Conversion and Management, 2012, 59(7): 1-8. [13] J.M. Calm, G.C. Hourahan. Refrigerant data summary. Engineered Systems, 2001, 18(11): 74-88. [14] J.F. Chen, C. Yang. Comparison of environmentally benign refrigerants R410A and R407C. Fluid Machinery, 2005, 33(7): 78-81. (only in Chinese) [15] H.Y. Zhang, J.M. Li, N. Liu, B.X. Wang. Experimental investigation of condensation heat transfer and pressure drop of R22, R410A and R407C in mini-tubes. International Journal of Heat and Mass Transfer, 2012, 55(13-14): 3522-3532. [16] C.H. Son, H.K. Oh. Condensation pressure drop of R22, R134a and R410A in a single circular microtube. Heat and Mass Transfer, 2012, 48(8): 1437-1450. [17] J. Kaew-On, S. Wongwises. Experimental study of evaporation heat transfer characteristics and pressure drops of R410A and R134a in a multiport mini-channel. Proceedings of the 7th International Conference on Nanochannels, Microchannels, and Minichannels, 2009, Part A: 581-588. [18] D. Huang, Q.X. Li. Performance comparison of evaporator with circuit number change in heat pump using R22 and R410A. Journal of Xi'an Jiaotong University, 2009, 43(7): 58-62. (only in Chinese) [19] C.Y. Park, P. Hrnjak. Experimental and numerical study on microchannel and round-tube condensers in a R410A residential air-conditioning system. International Journal of Refrigeration, 2008, 31(5): 822-831. [20] W. Chen. A comparative study on the performance and environmental characteristics of R410A and R22 residential air conditioners. Applied Thermal Engineering, 2008, 28(1): 1-7. [21] X.D. Wang, Y. Hwang, R. Radermacher. Two-stage heat pump system with vapor-injected scroll compressor using R410A as a refrigerant. International Journal of Refrigeration, 2009, 32(6): 1442-1451. [22] M. Karkri, R. Boussehain, M.L. Feidt, F. Sicard. Exergy analysis of a vapour-compression refrigerating system using R410A as refrigerant. International Journal of Exergy, 2009, 6(3): 295-322. [23] E. Elgendy, J. Schmidt, A. Khalil, M. Fatouh. Performance of a gas engine heat pump (GEHP) using R410A for heating and cooling applications. Energy, 2010, 35(12): 4941-4948. [24] X.L. Cao, S.X. Yu, L.X. Li, W. Wang, S.M. Liao. Theoretic and experimental study on domestic air-conditioner with R410A as refrigerant. 17

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Journal of Central South University (Science and Technology), 2010, 41(2): 759-763. (only in Chinese) [25] E. Elgendy, J. Schmidt, A. Khalil, M. Fatouh. Modelling and validation of a gas engine heat pump working with R410A for cooling applications. Applied Energy, 2011, 88(12): 4980-4988. [26] C.W. Roh, M.S. Kim. Comparison of the heating performance of an inverter-driven heat pump system using R410A vapor-injection into accumulator and compressor. International Journal of Refrigeration, 2012, 35(2): 434-444. [27] M.R. Ally, J.D. Munk, V.D. Baxter, A.C. Gehl. Exergy analysis and operational efficiency of a horizontal ground-source heat pump system operated in a low-energy test house under simulated occupancy conditions. International Journal of Refrigeration, 2012, 35(4): 1092-1103. [28] H.W. Jung, H. Kang, W.J. Yoon, Y. Kim. Performance comparison between a single-stage and a cascade multi-functional heat pump for both air heating and hot water supply. International Journal of Refrigeration, 2013, 36(5): 1431-1441. [29] G.L. Ding, C.L. Zhang, L. Zhao. New refrigerant for air conditioning in refrigeration . Shanghai: Shanghai Jiaotong University Press, 2003: 28-48. (only in Chinese) [30] F.D. Monte. Calculation of thermodynamic properties of R407C and R410A by the Martin – Hou equation of state: Part II Technical interpretation. International Journal of Refrigeration, 2002, 25(3): 314-329. [31] M.O. McLinden, S.A. Klein, E.W. Lemmon, et al. NIST REFPROP V7.0. USA: National Institute of Standards and Technology, 2006. [32] S. Ito, N. Miura. Studies of radiative cooling systems for storing thermal energy. Solar Energy Engineering, 1989, 111(3): 251-256. [33]S. Ito, N. Miura, K. Wang. Performance of a heat pump using direct expansion solar collectors. Solar Energy, 1999, 65(3):189-196. [34] E. Evyater, E. Yair. Radiative cooling of buildings with flat-plat solar collectors. Building and Environment, 2000, 35(4): 297-305. [35] J.A. Duffie, W.A. Beckman. Solar engineering of thermal process. New York: John Wiley and Sons, 1991: 250-331. [36] Y.Z. Wu. Miniature refrigeration equipment design guidelines. Beijing: Machinery Industry Press, 2004: 66-214. (only in Chinese) [37] F. Qiu, B. Gu, W.P. Zeng, et al. Simulation on heat transfer and pressure drop of R410A two-phase flow in plate heat exchanger. Journal of Refrigeration, 2010, 31(1): 39-44. (only in Chinese) [38] X.Q. Ma, G.L. Ding, P. Zhang, M.Y. Zhang. An experimental validation of void fraction models for R410A air-conditioner. Journal of Shanghai Jiaotong University, 2007, 41(3): 388-392. (only in Chinese) [39] Z.C. Qing. Simulation and experimental research of air-source heat pump with the refrigerant R410A. Nanjing: Nanjing Normal University, 2007, 18-33. (only in Chinese)

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Figure captions: Fig. 1. Schematic diagram of the DX-SAHP system using R410A Fig. 2. Cross-section in infinitesimal pipe of the collector/evaporator Fig. 3. Solution algorithm for predicting DX-SAHP system performance Fig. 4. Effect of refrigerant charge quantity on compressor power Fig. 5. Effect of refrigerant charge quantity on heating time Fig. 6. Effect of refrigerant charge quantity on useful energy gain of the collector Fig. 7. Effect of refrigerant charge quantity on collector instantaneous thermal efficiency Fig. 8. Effect of refrigerant charge quantity on instantaneous coefficient of performance Fig. 9. Effect of solar radiation intensity on system performance Fig. 10. Effect of ambient temperature on system performance Fig. 11. Effect of compressor rotational speed on system performance Fig. 12. Effect of initial water temperature on system performance

19

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S olar R ad iation

C ondenser C om pressor W ater T ank

C ollector/evaporator

E lectro nic E x pan sio n V alve

Fig. 1 S olar (an d/or am b ient) en ergy

T r,o , h r,o

T r,i , h r,i

l

Fig. 2.

20

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S tart

Inp ut structu re p aram eters, m eteo ro lo gical param eters, an d th e in itial w ater tem p erature in the h ot w ater tank

Inp ut the set v alues: tim e step , th e final w ater tem p erature in the h ot w ater tan k, the sup erheat d eg ree at the o utlet of th e co llecto r/ev ap orator and refrigerant charge

G uess evapo rating p ressure an d co nd ensing pressure

R un com presso r m o del: get m r , Wcom , and refrigerant state param eters at th e ou tlet o f th e co m p ressor

R un con denser m od el: get Q w , and refrigerant state param eters at th e ou tlet o f th e co nd enser

A d just cond ensing pressure

R un collector/evapo raotr m o del: get Q col , and refrigerant state param eters at th e in let of the collector/evapo rator

A d just evapo rating p ressure

E stim ated h e,i = h e,o ?

No

Y es A dd a tim e step

R un refrigerant charg e m o del: get M

No

r

E stim ated M r,cal = M r,set ? Y es

No

E stim ated t w ,cal = t w ,set ? Y es O utpu t final values

S top

Fig.3

21

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1.3 1.2

R410A Mr =1.48 kg

1.1

Mr =1.68 kg Mr =1.88 kg

W

com

(kW)

1.0

Mr =2.08 kg

0.9

Mr =2.28 kg

0.8 0.7 0.6 0.5 0.4 20

24

28

32

36

40

44

48

52

o

t ( C) w

Fig.4

80 70

R410A Mr =1.48 kg

60

Mr =1.68 kg Mr =1.88 kg

min)

50

Mr =2.08 kg

40

Mr =2.28 kg

30 20 10 0 20

24

28

32

36

40

44

48

52

o

t ( C) w

Fig. 5

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4.5 4.2

Q

col

(kW)

3.9 3.6 R410A

3.3

Mr =1.48 kg Mr =1.68 kg

3.0

Mr =1.88 kg Mr =2.08 kg

2.7

Mr =2.28 kg

2.4 20

24

28

32

36

40

44

48

52

o

t ( C) w

Fig. 6 1.4 1.3 1.2



k

1.1 1.0

R410A Mr =1.48 kg

0.9

Mr =1.68 kg Mr =1.88 kg Mr =2.08 kg

0.8

Mr =2.28 kg

0.7 20

24

28

32

36

40

44

48

52

o

t ( C) w

Fig. 7

23

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10 R410A

9

Mr =1.48 kg Mr =1.68 kg

8

COP

k

Mr =1.88 kg Mr =2.08 kg

7

Mr =2.28 kg

6 5 4 3 20

24

28

32

36

40

44

48

52

o

t ( C) w

Fig. 8 7

90  COP 

6

85

5 4 75 3

min)

, COP

80

70 2 65

1 0 200

300

400

500

600

700

800

900

60 1000

-2

I (W m )

Fig. 9 7

90  COP 

6

85

5 4 75 3

(min)

, COP

80

70 2 65

1 0 -5

0

5

10

15

20

25

30

35

60 40

o

t ( C) a

Fig. 10

24

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12

110  COP 

10

100

8

(min)

, COP

90 6 80 4 70

2

0

60 1500

1800

2100

2400

2700

3000

3300

-1

N (r min )

7

110

6

100

5

90

4

80  COP 

3

70

2

60

1

50

0 0

5

10

15

t

20

25

30

(min)

, COP

Fig. 11

40 35

o

w,ini

( C)

Fig. 12

25

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Table 1 Specification of the main components of the DX-SAHP system.

Name

Type

Remarks

Compressor

Rotary-type and hermetic

Rated input power: 0.75 kW, Displacement volume:13.4 cm3 rev-1

Water tank

Pressure

resistance

and

heat

150 L water, immersed 60 m serpentine copper tube (0.99×0.75 mm) as

insulation

condenser

Solar collector/evaporator

Aluminum plate, bare

4 plates in parallel 2 flow paths, total collector/evaporator area: 4.2 m2

Electronic expansion valve

ETS50B type,

External balance type

Table 2 Main parameters used in the performance calculation of the DX-SAHP water heater using R410A.

Compressor rotational speed (N)

2862 r min-1

Volumetric efficiency (φ)

0.91

Collector area (Acol)

4.2 m2

Thermal conductivity of collector plate (λp)

236 W m-1 K-1

Thickness of collector plate (δp)

4 mm

External diameter of the pipes in collector plate (D)

9.4 mm

distance of the pipes in collector plate (w)

40 mm

Absorptivity of collector plate (θ)

0.9

Emissivity of collector plate (ε)

0.1

Total efficiency of the compressor (ηcom)

0.75

polytropic index of the refrigerant vapor (κ)[39]

1.23

Specific heat of water(Cw)

4.18 kJ kg-1 K-1

Heat leakage coefficient of water tank(ζ)

0.95

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Water volume of hot water tank (Vw)

150 L

Thickness of polyurethane insulation (δ)

38 mm

Initial water temperature (tw,ini)

20.5 °C

Final water temperature (tw,f)

50 °C

Refrigerant charge quantity (Mr)

1.68 kg

Intensity of solar radiation (I)

750 W m-2

Ambient air temperature(ta)

25.7 °C

Wind speed (uw)

3.1 m s-1

Pipe length between compressor and condenser

1.5 m (9.15 mm ID)

Pipe length between condenser and electronic expansion valve

1.5 m (7 mm ID)

Pipe length between electronic expansion valve and collector

2.5 m (9 mm ID)

Pipe length between collector and compressor

2.5 m (9.4 mm ID)

Time step size

60 s

27

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